What is recorded here?
For a strictly increasing positive-integer sequence whose counting function eventually exceeds N^theta for every theta<1, concatenating its base-b representations gives a b-normal real. This proves the prime-concatenation example and the sums-of-two-squares example using the stated counting estimates.
Source-linked catalogue note. A detailed explanatory guide has not yet been prepared for this entry.
Scientific scope
Fixed-base normality of the corresponding constructed real, not absolute normality of the same decimal in every base or algorithmic randomness. The polynomial-value and simultaneous-base assertions at the end are conjectures, not proved here. Not absolute normality or algorithmic randomness. Finite leading digits do not alter normality. Besicovitch and Borel counting ingredients and Champernowne earlier construction keep credit; later polynomial and simultaneous-base paragraphs are explicitly conjectural in this source.
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People and systems
Arthur H. Copeland; Paul Erdős
Source-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.
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Documented countries / regions: United States
Printed University of Michigan common author address on the original final page. No nationality or individual effort share inferred.
English catalogue narrative
Copeland–Erdős normality of prime and sufficiently dense integer concatenations
For a strictly increasing positive-integer sequence whose counting function eventually exceeds N^theta for every theta<1, concatenating its base-b representations gives a b-normal real. This proves the prime-concatenation example and the sums-of-two-squares example using the stated counting estimates.
Scientific scope
Fixed-base normality of the corresponding constructed real, not absolute normality of the same decimal in every base or algorithmic randomness. The polynomial-value and simultaneous-base assertions at the end are conjectures, not proved here. Not absolute normality or algorithmic randomness. Finite leading digits do not alter normality. Besicovitch and Borel counting ingredients and Champernowne earlier construction keep credit; later polynomial and simultaneous-base paragraphs are explicitly conjectural in this source.
Reading status
This is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.
People and systems
Arthur H. Copeland; Paul Erdős
Source-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.